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Mat. Sb., 2000, Volume 191, Number 10, Pages 87–104 (Mi msb517)  

This article is cited in 1 scientific paper (total in 1 paper)

Two-dimensional manifolds with metrics of revolution

I. Kh. Sabitov

M. V. Lomonosov Moscow State University

Abstract: This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in $\mathbb R^3$ other than a sphere and a torus (moreover, in the smoothness class $C^\infty$ such surfaces, understood in a certain generalized sense, exist in any topological class).

DOI: https://doi.org/10.4213/sm517

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English version:
Sbornik: Mathematics, 2000, 191:10, 1507–1525

Bibliographic databases:

UDC: 513.73
MSC: Primary 53A05; Secondary 57N05
Received: 09.12.1999

Citation: I. Kh. Sabitov, “Two-dimensional manifolds with metrics of revolution”, Mat. Sb., 191:10 (2000), 87–104; Sb. Math., 191:10 (2000), 1507–1525

Citation in format AMSBIB
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\by I.~Kh.~Sabitov
\paper Two-dimensional manifolds with metrics of revolution
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 10
\pages 87--104
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\crossref{https://doi.org/10.4213/sm517}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1817121}
\zmath{https://zbmath.org/?q=an:0981.53007}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 10
\pages 1507--1525
\crossref{https://doi.org/10.1070/sm2000v191n10ABEH000517}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034341601}


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  • http://mi.mathnet.ru/eng/msb/v191/i10/p87

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. Kh. Sabitov, “Isometric surfaces with a common mean curvature and the problem of Bonnet pairs”, Sb. Math., 203:1 (2012), 111–152  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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